there should be an explicit option to switch between the modes.
I agree, and don't really care which one is default
Yes, an option makes sense.
And it can happen that the same person wants both behaviors at
different times.
Indeed. This goes back to the ambiguity of `narrow-to-region', which
can be used either to "pretend the rest of the buffer doesn't exist" (as
was used in Rmail for example), or to "temporarily focus on some
particular part of the buffer without pretending the rest doesn't
exist".